given the assumption that \(\left\Vert A^{(L)}\right\Vert _{F, \infty } \le c_A L^{-1/2}\) . The proof can be found in Appendix . Note that the bounds are deterministic, unlike the probabilistic results from [1]}, [2]}. Next, we derive that the norm of the gradient of the objective function is bounded above by \(J_L(A^{(L)})^{1/2}\) , so that it ensures that the gradient updates (REF ) stay local. The precise result and its proof can be found in Appendix .
